Tridimensional visualization of the Verhulst dynamics [*Visualisation tridimensionnelle de la dynamique de Verhulst*].

The Verhulst dynamics is defined using the following iteration:
X = 0.5
0

X = RX (1 - X )
n n-1 n-1

Here, in this computation, the growing rate 'R' is no longer constant but changes its value periodically
using the following arbitrary cycle:
R3 ==> R3 ==> R3 ==> R3 ==> R2 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1

(based on the sine function on [0,8.pi])
where {R1,R2,R3} are respectively the three coordinates of the current point
inside the following domain [2.936,3.413]x[3.500,3.850]x[3.000,4.000].
Only the points corresponding to a dynamical system with **a negative Lyapunov exponent** are displayed.

See a set of 4x3 stereograms:

See a bidimensionnal dynamics:

(CMAP28 WWW site: this page was created on 11/23/2010 and last updated on 10/27/2015
10:53:31 -CET-)

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Copyright (c) Jean-François Colonna, 2010-2015.

Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2015.